An apparatus and method for measuring the viscosity of Newtonian and non-Newtonian fluids over a range of shear rates, especially low shear rates, by monitoring two rising columns of fluid (Newtonian or non-Newtonian) that pass through respective capillaries having different lengths. Furthermore, a specialized column monitor is provided that uses multiple interrogation sources (e.g., lasers) and a single detector (e.g., a charge-coupled device (CCD) array) to continuously monitor both columns of fluid substantially simultaneously. In particular, the system includes a Y-connector to form two flow paths and wherein each flow path includes a tube that includes a riser tube, a capillary tube of predetermined dimensions and a valve in each for controlling the fluid flow in each path. The specialized column monitor monitors the movement of the fluid columns in each of the riser tubes and an associated microprocessor analyzes these movements, along with the predetermined dimensions of the capillary tubes and riser tubes to determine the viscosity of the fluid.